(a) Consider an insurer that oers 2 types of policy: home insurance and car insurance. 70% of all customers have a home insurance policy, and 80% of all customers have a car insurance policy. Every customer has at least one of the two types of policies.

Calculate the probability that a randomly selected customer

(i) does not have a car insurance policy, (1)

(ii) has car insurance and home insurance, (1)

(iii) has home insurance, given that he has car insurance, (2)

(iv) does not have car insurance, given that he has home insurance. (2)

(b) A statistician is examining the survey methodology of a country's national statistics department. It conducts much of its data collection by telephoning individuals selected at random and asking them questions.

(i) Comment on whether this methodology will give a random sample. (2)

(ii) Comment on whether this methodology will give a representative sample of the population. (2)

(c) In a study to compare two dierent methods of teaching reading, a class of thirty children was divided into two groups at random. Each group was taught reading using one method. After six months the two groups were given the same test. One pupil in the first group was ill and missed the test. The scores are given below.

Method 1; 80 85 79 81 89 73 50 71 76 87 72 85 86 85 Method 2; 79 62 75 68 62 73 76 81 73 61 72 68 75 63 62

(i) Calculate the extreme values and the quantiles for each group. (7)

(ii) Hence draw box-and-whisker plots for the two groups using the same scale. (2)

(iii) Comment on the dierences between the two groups. (2)

(d) In the claims department of an insurance oce various quantities are computed at the end of each day's business. On Monday, 10 claims are received for a particular class of policy. The mean claim amount is calculated to be $4,260 and the standard deviation to be $1,120.

On Tuesday it is found that one of Monday's claims for $5,450, was classied wrongly and it is removed from the set of 10 claims. Calculate the resulting mean and standard deviation of the reduced set of 9 claims.